The difference of boundary effects between Bose and Fermi systems

TL;DR

This paper investigates the fundamental differences in boundary effects between Bose and Fermi systems under various temperature and density conditions, revealing distinct dependencies and proposing a modified virial expansion for high-temperature regimes.

Contribution

It identifies the contrasting boundary influences in Bose and Fermi systems and introduces a modified virial expansion to accurately compute boundary effects at high temperatures.

Findings

Boundary effects depend on temperature for Bose systems but on density for Fermi systems.

At high temperatures and low densities, boundary influence differences appear in next-to-leading order terms.

A modified virial expansion is proposed for high-temperature, low-density boundary effect calculations.

Abstract

In this paper, we show that there exists an essential difference of boundary effects between Bose and Fermi systems both for Dirichlet and Neumann boundary conditions: at low temperatures and high densities the influence of the boundary on the Bose system depends on the temperature but is independent of the density, but for the Fermi case the influence of the boundary is independent of the temperature but depends on the density, after omitting the negligible high-order corrections. We also show that at high temperatures and low densities the difference of the influence of the boundary between Bose and Fermi systems appears in the next-to-leading order boundary contribution, and the leading boundary contribution is independent of the density. Moreover, for calculating the boundary effects at high temperatures and low densities, since the existence of the boundary modification causes the standard virial expansion to be invalid, we introduce a modified virial expansion.